Therefore the demand function h (p, u) keeps the consumer’s utility level fixed as prices change. In contract with the Walrasian demand function it keeps money wealth fixed but allows utility to vary.

We derive the Hicksian demand curve by projecting the demand for x downwards into the demand curve diagram. Notice that the Hicksian demand curve is steeper than the Marshallian demand curve when the good is a normal good. So they will choose a new equilibrium point on a higher indifference curve.

Qd = a – b(P)

1. Q = quantity demand.
2. a = all factors affecting price other than price (e.g. income, fashion)
3. b = slope of the demand curve.
4. P = Price of the good.

Derive the demand function, which sets the price equal to the slope times the number of units plus the price at which no product will sell, which is called the y-intercept, or “b.” The demand function has the form y = mx + b, where “y” is the price, “m” is the slope and “x” is the quantity sold.

If we assume that the consumer has Cobb-Douglas utility function over the two goods. That is u (x 1 ,x 2) = x 1a x 11-a. By deriving the first order conditions for the EMP and substituting from the constraints u (h 1 (p, u), h 2 (p, u) = u, we obtain the Hicksian demand functions.

We can solve for the Marshallian demand function for x directly from the first equation: x ∗ = f ′ − 1 ( P x P y). y ∗ = I − P x f ′ − 1 ( P x P y) P y.

Then for any p » 0, the Hicksian demand correspondence h (p, u) possesses the following two properties. Homogeneity of degree zero in P follow because the optimal vector. The minimizing p.x is subject to u (x) ≥ u. It is same as that for minimizing ∝p.x. It is subject to this constraint for any scalar ∝ > 0.